Does a Gas-Filled Bottle Oscillate Underwater Due to Pressure Changes?

[sgstudent]

When I place a bottle of gas underwater where the pressure is higher, the force exerted on the outside surface of the bottle increases. So the gas inside would have to exert an greater force than before to equalize that external force. So would that process of decreasing volume to jncrease the force (hence pressure) showcase Boyle's Law where as volume decreases the pressure increases?

Also, after the force outside and inside equalizes (no net force) the volume of the container should stop decreasing right? But since there's no net force shouldn't there be a constant velocity? If so shouldn't the volume continue to decrease?

Or now that it decreases even a little, then the pressure inside is slightly greater than of the outside so the pressure causing a net force in the other direction. Causing the bottle to expand a little again. So would this mean that the volume would continuously expand and contract?

Thanks for the help :)

 

[sophiecentaur]

The answer to this will depend upon the bottle. Is it 'ideal' (i.e. rigid)? If it flexes then the amount by which its volume decreases will depend upon its modulus / thickness etc.. The limiting case would be a plastic bag, for which the internal gas pressure would be the same as the ambient pressure. You'd need some numbers if you want more of an answer, I think.

 

[sgstudent]

The answer to this will depend upon the bottle. Is it 'ideal' (i.e. rigid)? If it flexes then the amount by which its volume decreases will depend upon its modulus / thickness etc.. The limiting case would be a plastic bag, for which the internal gas pressure would be the same as the ambient pressure. You'd need some numbers if you want more of an answer, I think.

Hi what do you mean by an ideal bottle? Is it because if the bottle is able to withstand some external force then the bottle won't decrease in volume as much?

Oh in this case, I'm assuming the bottle to change perfectly to the pressure outside of it. But since if we look at the forces once the bottle decreased in volume to the amount that the external force is equal to the internal force, then shouldn't the bottle have a certain velocity when the net force equals zero? So wouldn't that cause the bottle to continue moving inwards at a certain velocity?

Thanks for the reply :)

 

[sophiecentaur]

Hi what do you mean by an ideal bottle? Is it because if the bottle is able to withstand some external force then the bottle won't decrease in volume as much?

Oh in this case, I'm assuming the bottle to change perfectly to the pressure outside of it. But since if we look at the forces once the bottle decreased in volume to the amount that the external force is equal to the internal force, then shouldn't the bottle have a certain velocity when the net force equals zero? So wouldn't that cause the bottle to continue moving inwards at a certain velocity?

Thanks for the reply :)

The "net force" will be in the other direction once the bottle goes past its equilibrium diameter and the result will be to maintain the bottle at its equilibrium dimension - which will be, in some way, inversely related to the ambient pressure. This is analogous to a mass hanging on a spring, with a weaker spring pulling it down. As you change the force on the upper spring, you will arrive at a new equilibrium situation.
In real life, you could expect a certain amount of oscillation after the change, which will decay due to friction loss.

 

[sgstudent]

The "net force" will be in the other direction once the bottle goes past its equilibrium diameter and the result will be to maintain the bottle at its equilibrium dimension - which will be, in some way, inversely related to the ambient pressure. This is analogous to a mass hanging on a spring, with a weaker spring pulling it down. As you change the force on the upper spring, you will arrive at a new equilibrium situation.
In real life, you could expect a certain amount of oscillation after the change, which will decay due to friction loss.

Oh would that 'oscilation' represent the continuous upwards force, then changes to a downwards force repeated?

If so, how would it decay over time? Because if so shouldn't it continuously vibrate up and down for a long time?

Thanks so much for the help :)

 

[sophiecentaur]

Oh would that 'oscilation' represent the continuous upwards force, then changes to a downwards force repeated?

If so, how would it decay over time? Because if so shouldn't it continuously vibrate up and down for a long time?

Thanks so much for the help :)

If you look at the many oscillating systems around you (pendulum, guitar string, standing on diving board etc. etc.) you can see that there is an equilibrium position and that, once you displace the mass (etc.) there is a net force taking it back to that position (a 'restoring force'). The further away from equilibrium position, the stronger the force. Look up 'harmonic oscillator' and find a link to suit your level, if you want some more info about it.
Any movement of anything involves some friction mechanism or loss, so the oscillations will gradually die down as the energy is dissipated. You will recognise this in everyday life. Even a really heavy pendulum on a steel wire will eventually slow down and stop because energy is lost. Otoh, a motor car suspension will only deform for up to a cycle of bounce, because the dampers dissipate the energy very quickly.
In the case of your 'bottle' experiment, the rate of energy dissipation would depend upon the material of the bottle and the speed of the initial pressure change. You could imagine a 'ringing' with a thin walled steel bottle, possibly. For a slow initial change of pressure, you wouldn't expect any ringing at all and changes could be treated as 'quasi static'.